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These two pendulums in SHM

  1. Sep 11, 2014 #1
    1. The problem statement, all variables and given/known data
    In a thread with a sphere of mass M on one end, another thread BC is suspended with a sphere of mass m (as the image below). The point A executes small oscillations in the horizontal of period T. Find the length L of BC, knowing that B remains straight underneath A at all time

    20140911_033630-1.jpg

    2. Relevant equations
    SHM and dynamics equations

    3. The attempt at a solution
    As AB is always on the vertical, we can see that when A is pushed to one side, BC hangs to the same side in order to balance the angular momentum. So, adopting the non inertial reference of AB, the sphere of mass m is now affected by the weight and the force that pushed A, let's say F. Then I've tried to analyze the forces in the direction of the mass' m movement to prove the simple harmonic motion of the system. But how can I calculate F? I can't seem to describe it mathematically :/
     
    Last edited: Sep 11, 2014
  2. jcsd
  3. Sep 11, 2014 #2

    BvU

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    confuses me no end. Can I interptret this as: B remains straight underneath A at all time?
     
  4. Sep 11, 2014 #3
    Yes, this is what you should interpret, actually. Let me edit the post
     
    Last edited: Sep 11, 2014
  5. Sep 11, 2014 #4

    BvU

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    So for all I kn
    ow AB could just as well be a stiff bar, right ?
     
  6. Sep 12, 2014 #5
    Yes, despise their mass and consider they are a stiff bar
     
  7. Sep 12, 2014 #6

    BvU

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    BC can be any length at all, there's nothing to restrict it: nothing is being said about C !
     
  8. Sep 12, 2014 #7
    Probably not. Imagine, for an instance, |BC| >> |AB| and m>>M, then the period of oscillation must be smaller to compensate the angular momentum and to keep AB in the vertical. So I guess there must be a relation between the masses, period and BC's length as the problem requests
     
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